_ The mystery of form is one of nature’s deepest secrets. It has attracted some of the greatest minds, both scientific and artistic, from Aristotle through Leonardo and Durer in the Renaissance, to Alan Turing in the 20th century.

Form and pattern are the natural meeting place of art and science so why is it that we don’t know more about this magic land where the lion of science lies down with the lamb of art? The reason is the strange status of form in science – its relative neglect. Darwin wrote of ‘Endless forms most beautiful’. But he knew nothing of the processes that created these forms: natural selection is a sieve of possible forms, not the generating mechanism itself.

It is only in the last 30 years that biological pattern-making has come of age. But, as with every subject, there is a pre-history. There are unsung pioneers.

The undisputed prophet of biological form is D’Arcy Wentworth Thompson (1860-1948). Thompson was a great Victorian, Scottish polymath. I say Victorian although he died in 1948. But everything about Thompson was redolent of 19th century genius. He was a mathematician and a classicist as well as a biologist. He was regarded as being outside the biological mainstream until the new science of biological form, evo devo, took off in the 1980s. Thompson didn’t like the indirectness of Darwinian natural selection. He thought that physical forces acted directly on living things to shape them.

He showed how soapy foams template the intricate geometrical forms of the marine creatures, radiolarians. There is a whole geometry that connects soap bubbles, the radiolarians, bees’ honeycombs, the football, Buckminster fuller’s domes and the C60 molecule named after Fuller: buckminsterfullerene. And Thompson was the first to demonstrate it.

The second great prophet of morphology is the mathematician and computer pioneer Alan Turing. In 1952 almost nothing concrete was known about the biological mechanism of pattern formation but the problem interested one of the greatest minds of the century. Like D’Arcy Thompson, Turing noticed patterns in living things that could be explained by physical processes.

Long before chaos theory, Turing showed mathematically how chemicals diffusing through biological tissue and reacting could become unstable and lead to complex patterns such as the markings on snail shells, leopards, jaguars, giraffes, and Friesian cattle.

Many of the patterns in nature can be generated by algorithms, equations that feed back in to themselves. In nature it is not equations that feed upon each other but systems of activation and inhibition. You can see this in a purely chemical reaction – the Belousov-Zhabotinsky reaction – that produces ever changing patterns. Some of these patterns can also be seen in nature, for example in slime moulds. The convergence of mathematics, chemistry and natural forms demonstrates a powerful principle that governs all pattern formation.

This convergence also embraces art. Thompson saw parallels between natural processes such as the formation of gourds and technical processes like glass blowing: in each the shape results from an interplay of physical forces. So D’Arcy Thompson regarded beauty as the product of graded curves that shift in a smooth manner from one radius to another. He wrote:

“The Florence flask or any other handiwork of the glassblower is always beautiful because its graded contours are, as in its living analogues, a picture of the graded forces by which it was conformed. It is an example of mathematical beauty.”

Then there’s Sir Ernst Gombrich, a great art critic who found parallels between natural and human creativity: he wrote beautifully on mimicry and what nature’s copying and stylized warnings mean for the art of human beings: “For the evolution of convincing images was indeed anticipated by nature long before human minds could conceive this trick . . . the art historian and the critic could do worse than ponder these miracles. They will make him pause before he pronounces too glibly on the relativity of standards that make for likeness and recognition.”

Gombrich finds various styles of art in nature: a leaf butterfly can fancifully be considered to be “a naturalistic artist,” natural selection having produced a facsimile of the dead-leaf pattern. But the eyespots sported by some butterflies are stylized gestures: “They represent, if you like, the Expressionist style of nature.”

The study of beauty in nature and human art is suddenly a live subject again. I have written about parallels between art and nature in The Gecko’s Foot and Dazzled and Deceived. Philip Ball brilliantly brings D’Arcy Thompson up to date in Shapes, one of three volumes spun off from his magisterial survey The Self-Made Tapestry: Pattern Formation in Nature. In 2009 The Fitzwilliam Museum in Cambridge mounted a seminal exhibition on Darwin and the visual arts, which produced a sumptuous volume: Endless Forms: Natural Science and the Visual Arts. And now in Survival of the Beautiful David Rothenberg surveys the field of nature’s artists, finding parallels between abstract art and the patterns of creatures such as the bower birds and squid.

Somewhere to the side of the Saatchi/Turner/Hirst/Emin axis, a new force in visual art is stirring.

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I'm a writer whose interests include the biological revolution happening now, the relationship between art and science, jazz, and the state of the planet